Unfortunately, the Visibility property isn't available in v5.5. You'd have to create a custom page for this and define the edit form within the doc types properties on the General tab. What this means is you'd create an alternative form (suggest 1 for each site), then create a physical page in the file system which would inherit the CMSDeskPage class (I believe). Then in the code behind load the object information and set the form definition to the alternative form for the site that is currently being accessed.
What I would do is create my alternative forms in a similar fashion so I don't have to hard code anything. For instance, if my site code name is MySite, I'd name my alternative form DocTypeEditMySite. Then in code, I can gather my alternative form by using
form.AlternativeForm = "DocTypeEdit" + CurrentSite.SiteCodeName (which would render DocTypeEditMySite).
All the code is psudo, so you'd have to see what it actually would look like for the version you are on. I'd suggest looking in the file system in the /CMSModules/DocumentTypes/Pages to start, there should be some examples of how you'd get started in there. Remember to create your own set of pages though, don't modify the base ones.